In Table REF , we present the results for \(\alpha _d\)  and \(\alpha _q\)  from our RNCCSD method along with results from our DF, MBPT(2), MBPT(3), RPA and RCCSD methods. If we compare the results from all these methods apart from the RNCCSD method with that are reported in Ref. [1]}, we find that the results are slightly different at the given level of approximation.
In Ref. [1]} contributions from partial triple excitations were considered in the RCCSD calculation (CCSD\(_p\) T) method, but the main reason for discrepancy in the result from the present work is owing to the use of optimized basis functions. A slightly large difference is seen at the MBPT(3) method because of consideration of contributions from a few additional Goldstone diagrams here which were not included in Ref. [1]}. The RNCCSD results are given for the first time. The trends of the \(\alpha _d\)  and \(\alpha _q\)  values through different many-body methods are shown pictorially in Fig. REF  after normalizing with their respective DF values. As can be seen from the above table and from the figure, the difference between the DF and RNCCSD values for \(\alpha _d\)  is small but there is a relatively large difference for the \(\alpha _q\)  value from these methods. This implies that the electron correlation trends between both the properties are different. In fact, results from the lower-order methods show that the \(\alpha _d\)  and \(\alpha _q\)  values increase in the MBPT(2) method compared to the DF values, while their magnitudes reduce slightly in the MBPT(3) method. As it was mentioned earlier, the MBPT(2) method contains the lowest-order RPA correlation terms while the MBPT(3) method introduces the lowest-order non-RPA correlation terms. Thus, the above trends in the results from the MBPT(2) and MBPT(3) methods suggest that there are cancellations in the correlation contributions arising through the RPA and non-RPA types of correlations. This is further evident from the RPA and RCCSD results. The RPA, which accounts for correlation contributions due to all-order core-polarization effects, give very large values for both \(\alpha _d\)  and \(\alpha _q\) . However, the RCCSD results are close to the MBPT(3) values. This means that the core-polarization effects enhance the magnitudes of both the polarizabilities while other correlation effects contribute with opposite signs at the all-order perturbation level. We also observe that these cancellations are slightly larger (in percentage) for \(\alpha _q\)  than \(\alpha _d\) . Comparing results from the RCCSD and RNCCSD methods, the differences in \(\alpha _d\)  and \(\alpha _q\)  from both the methods are found to be about 3% and 1% respectively. In the above table, we have also given \(B\)  values but only from the DF, RCCSD and RNCCSD methods. The reason for not giving results from the other lower methods is that the theoretical evaluation of \(B\)  depends on the first-order wave functions due to \(D\)  and \(Q\) , so by analysing results for \(\alpha _d\)  and \(\alpha _q\)  using lower-order methods propagation of electron correlation effects from lower-order to all-order methods can be understood.
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